Confonner

It would appear that identical particle pemuitation groups are not of help in providing distinguishing syimnetry labels on molecular energy levels as are the other groups we have considered. However, they do provide very usefiil restrictions on the way we can build up the complete molecular wavefiinction from basis fiinctions. Molecular wavefiinctions are usually built up from basis fiinctions that are products of electronic and nuclear parts. Each of these parts is fiirther built up from products of separate uncoupled coordinate (or orbital) and spin basis fiinctions. Wlien we combine these separate fiinctions, the final overall product states must confonn to the pemuitation syimnetry mles that we stated above. This leads to restrictions in the way that we can combine the uncoupled basis fiinctions. 

Free energy perturbation (FEP) theory is now widely used as a tool in computational chemistry and biochemistry [91]. It has been applied to detennine differences in the free energies of solvation of two solutes, free energy differences in confonnational or tautomeric fonns of the same solute by mutating one molecule or fonn into the other. Figure A2.3.20 illustrates this for the mutation of CFt OFl CFt CFt [92]. 

An essential feature of mean-field theories is that the free energy is an analytical fiinction at the critical point. Landau [100] used this assumption, and the up-down symmetry of magnetic systems at zero field, to analyse their phase behaviour and detennine the mean-field critical exponents. It also suggests a way in which mean-field theory might be modified to confonn with experiment near the critical point, leading to a scaling law, first proposed by Widom [101], which has been experimentally verified. 

In the above discussion it was assumed that the barriers are low for transitions between the different confonnations of the fluxional molecule, as depicted in figure A3.12.5 and therefore the transitions occur on a timescale much shorter than the RRKM lifetime. This is the rapid IVR assumption of RRKM theory discussed in section A3.12.2. Accordingly, an initial microcanonical ensemble over all the confonnations decays exponentially. However, for some fluxional molecules, transitions between the different confonnations may be slower than the RRKM rate, giving rise to bottlenecks in the unimolecular dissociation [4, ]. The ensuing lifetime distribution, equation (A3.12.7), will be non-exponential, as is the case for intrinsic non-RRKM dynamics, for an mitial microcanonical ensemble of molecular states. 

Figure Bl.5.7 displays results of a measurement of the rotational anisotropy for an oxidized Si(l 11) surface [65]. For the case shown in the top panel, the results confonn to the predictions of equation Bl.5.42 (with/...

These chain models are well suited to investigate the dependence of tire phase behaviour on the molecular architecture and to explore the local properties (e.g., enriclnnent of amphiphiles at interfaces, molecular confonnations at interfaces). In order to investigate the effect of fluctuations on large length scales or the shapes of vesicles, more coarse-grained descriptions have to be explored. 

Van der Waals complexes can be observed spectroscopically by a variety of different teclmiques, including microwave, infrared and ultraviolet/visible spectroscopy. Their existence is perhaps the simplest and most direct demonstration that there are attractive forces between stable molecules. Indeed the spectroscopic properties of Van der Waals complexes provide one of the most detailed sources of infonnation available on intennolecular forces, especially in the region around the potential minimum. The measured rotational constants of Van der Waals complexes provide infonnation on intennolecular distances and orientations, and the frequencies of bending and stretching vibrations provide infonnation on how easily the complex can be distorted from its equilibrium confonnation. In favourable cases, the whole of the potential well can be mapped out from spectroscopic data. 

Most properties of linear polymers are controlled by two different factors. The chemical constitution of tire monomers detennines tire interaction strengtli between tire chains, tire interactions of tire polymer witli host molecules or witli interfaces. The monomer stmcture also detennines tire possible local confonnations of tire polymer chain. This relationship between the molecular stmcture and any interaction witli surrounding molecules is similar to tliat found for low-molecular-weight compounds. The second important parameter tliat controls polymer properties is tire molecular weight. Contrary to tire situation for low-molecular-weight compounds, it plays a fimdamental role in polymer behaviour. It detennines tire slow-mode dynamics and tire viscosity of polymers in solutions and in tire melt. These properties are of utmost importance in polymer rheology and condition tlieir processability. The mechanical properties, solubility and miscibility of different polymers also depend on tlieir molecular weights. 

Polymer chains at low concentrations in good solvents adopt more expanded confonnations tlian ideal Gaussian chains because of tire excluded-volume effects. A suitable description of expanded chains in a good solvent is provided by tire self-avoiding random walk model. Flory 1151 showed, using a mean field approximation, that tire root mean square of tire end-to-end distance of an expanded chain scales as... 

Flow behaviour of polymer melts is still difficult to predict in detail. Here, we only mention two aspects. The viscosity of a polymer melt decreases with increasing shear rate. This phenomenon is called shear thinning [48]. Another particularity of the flow of non-Newtonian liquids is the appearance of stress nonnal to the shear direction [48]. This type of stress is responsible for the expansion of a polymer melt at the exit of a tube that it was forced tlirough. Shear thinning and nonnal stress are both due to the change of the chain confonnation under large shear. On the one hand, the compressed coil cross section leads to a smaller viscosity. On the other hand, when the stress is released, as for example at the exit of a tube, the coils fold back to their isotropic confonnation and, thus, give rise to the lateral expansion of the melt. 

Monte Carlo simulations generate a large number of confonnations of tire microscopic model under study that confonn to tire probability distribution dictated by macroscopic constrains imposed on tire systems. For example, a Monte Carlo simulation of a melt at a given temperature T produces an ensemble of confonnations in which confonnation with energy E. occurs witli a probability proportional to exp (- Ej / kT). An advantage of tire Monte Carlo metliod is tliat, by judicious choice of tire elementary moves, one can circumvent tire limitations of molecular dynamics techniques and effect rapid equilibration of multiple chain systems [65]. Flowever, Monte Carlo... 

A drop of a dilute solution (1%) of an amphiphile in a solvent is typically placed on tlie water surface. The solvent evaporates, leaving behind a monolayer of molecules, which can be described as a two-dimensional gas, due to tlie large separation between tlie molecules (figure C2.4.3). The movable barrier pushes tlie molecules at tlie surface closer together, while pressure and area per molecule are recorded. The pressure-area isotlienn yields infonnation about tlie stability of monolayers at tlie water surface, a possible reorientation of tlie molecules in tlie two-dimensional system, phase transitions and changes in tlie confonnation. Wliile being pushed togetlier, tlie layer at... 

Thermal stahility. Yor applications of LB films, temperature stability is an important parameter. Different teclmiques have been employed to study tliis property for mono- and multilayers of arachidate LB films. In general, an increase in temperature is connected witli a confonnational disorder in tire films and above 390 K tire order present in tire films seems to vanish completely [45, 46 and 45] However, a comprehensive picture for order-disorder transitions in mono- and multilayer systems cannot be given. Nevertlieless, some general properties are found in all systems [47]. Gauche confonnations mostly reside at tire ends of tire chains at room temperature, but are also present inside tire... 

The polymers described so far have relatively flexible main chains which can result in complex confonnations. In some cases, tliey can double back and cross over tliemselves. There are also investigations on polymers which are constrained to remain in a confonnation corresponding, at least approximately, to a straight line, but which have amphiphilic properties tliat ensure tliat tliis line is parallel to tire water surface. Chiral molecules are one example and many polypeptides fall into tliis class [107]. Another example is cofacial phtlialocyanine polymers (figure C2.4.9). 

The tliird part is tire interaction between tire tenninal functionality, which in tire case of simple alkane chains is a metliyl group (-CH ), and tire ambient. These surface groups are disordered at room temperature as was experimentally shown by helium atom diffraction and infrared studies in tire case of metliyl-tenninated monolayers [122]. The energy connected witli tliis confonnational disorder is of tire order of some kT. 

Thermal stability. The tliennal stability of SAMs is, similarly to LB films, an important parameter for potential applications. It was found tliat SA films containing alkyl chains show some stability before an increase in tire number of gauche confonnations occurs, resulting in melting and irreversible changes in tire film. The disordering of tire... 

Similarly to LB films, the order of alkanetliiols on gold depending on temperature has been studied witli NEXAFS. It was observed tliat tire barrier for a gauche confonnation in a densely packed film is an order of magnitude higher tlian tliat of a free chain [48]. 

Because this problem is complex several avenues of attack have been devised in the last fifteen years. A combination of experimental developments (protein engineering, advances in x-ray and nuclear magnetic resonance (NMR), various time-resolved spectroscopies, single molecule manipulation methods) and theoretical approaches (use of statistical mechanics, different computational strategies, use of simple models) [5, 6 and 7] has led to a greater understanding of how polypeptide chains reach the native confonnation. 

Given that a sequence folds to a known native stmcture, what are the mechanisms in the transition from the unfolded confonnation to the folded state This is a kinetics problem, the solution of which requires elucidation of the pathways and transition states in the folding process. 

The sequence space of proteins is extremely dense. The number of possible protein sequences is 20. It is clear that even by the fastest combinatorial procedure only a very small fraction of such sequences could have been synthesized. Of course, not all of these sequences will encode protein stmctures which for functional purjDoses are constrained to have certain characteristics. A natural question that arises is how do viable protein stmctures emerge from the vast sea of sequence space The two physical features of folded stmctures are (l)in general native proteins are compact but not maximally so. (2) The dense interior of proteins is largely made up of hydrophobic residues and the hydrophilic residues are better accommodated on the surface. These characteristics give the folded stmctures a lower free energy in comparison to all other confonnations. 

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